Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
 /*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */

import java.util.*;

public class FunkyNumbers {

    public static void main(String[] args) {

        Scanner scan = new Scanner(System.in);
        int num = scan.nextInt();
        int j = 1;
       HashSet<Integer> S = new HashSet<Integer>();

        for (int i = 1; i <= num; i++) {
            j = i * (i + 1) / 2;

            S.add(j);

            if (j > num) {
                break;
            }
        }

        boolean bandera = false;
        for (int i : S) {
            if (S.contains(num - i)) {
                bandera = true;
                break;
            }
        }
        if (bandera) 
            System.out.println("YES");
         else 
            System.out.println("NO");
        
    }
}